Advertisement

Directional Growth of Dilute Mixtures and Lamellar Eutectics

  • K. Kassner
  • C. Misbah
  • H. Müller-Krumbhaar
  • Y. Saito
  • D. E. Temkin
Part of the NATO ASI Series book series (NSSB, volume 284)

Abstract

Pattern formation in directional growth of dilute mixtures and eutectics is studied. In the cellular and dendritic problems, we compare our results on tip selection with the theory of a needle-shaped crystal in a channel. The selection of a dendrite is based either on surface tension or kinetics anisotropy. The possibility for the interface to undergo chaotic motion at large growth speeds is discussed. For lamellar eutectics we present recent results on a parity-breaking transition and similarity laws.

Keywords

Directional Growth Diffusion Length Planar Front Kinetic Coefficient Eutectic Growth 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J.S. Langer, in Proceedings of the Les Houches Summer School, Session 46, edited by J. Souletie, J. Vannimenus, and R. Stora (Elsevier, Amsterdam, 1987).Google Scholar
  2. 2.
    C. Misbah, H. Müller-Krumbhaar and D.E. Temkin, J. Physique 11, 585 (1991).Google Scholar
  3. 3.
    J.D. Hunt and K.A. Jackson , Trans. Metall. Soc. AIME 236, 843 (1966);Google Scholar
  4. V. Seetharaman and R. Trivedi, Metall. Trans. 19A., 2955 (1988).Google Scholar
  5. 4.
    G. Faivre, S. de Cheveigné, C. Guthmann, and P. Kurowski, Europhys. Lett. 9, 779 (1989).ADSCrossRefGoogle Scholar
  6. 5.
    A.J. Simon, J. Bechoefer and A. Libchaber, Phys. Rev. Lett. 61, 2574 (1988).ADSCrossRefGoogle Scholar
  7. 6.
    R. Racek, Thèse d’Université Nancy I, (1973);Google Scholar
  8. 6a.
    see also H.E. Cline, Mat. Sci. Engr. 65, 93 (1984).CrossRefGoogle Scholar
  9. 7.
    Y. Saito, G. Goldbeck-Wood, and H. Müller-Krumbhaar, Phys. Rev. A 38, 2148 (1988).ADSCrossRefGoogle Scholar
  10. 8.
    W.W. Mullins and R.F. Sekerka, J. Appl. Phys. 35, 444 (1964).ADSCrossRefGoogle Scholar
  11. 9.
    L.H. Ungar and R.A. Brown, Phys. Rev. B 29, 1367 (1984);ADSCrossRefGoogle Scholar
  12. 9a.
    L.H. Ungar and R.A. Brown, Phys. Rev. B 30, 3993 (1984);ADSCrossRefGoogle Scholar
  13. 9b.
    L.H. Ungar and R.A. Brown, Phys. Rev. B 31, 5923 (1985);ADSCrossRefGoogle Scholar
  14. 9c.
    L.H. Ungar and R.A. Brown, Phys. Rev. B 31, 5931 (1985).ADSCrossRefGoogle Scholar
  15. 10.
    Y. Saito, C. Misbah and H. Müller-Krumbhaar, Phys. Rev. Lett. 63, 2377 (1989).ADSCrossRefGoogle Scholar
  16. 11.
    P.G. Saffman and G.I. Taylor, Proc. R. Soc. A 245, 312 (1958).MathSciNetADSMATHCrossRefGoogle Scholar
  17. 11a.
    The analogy with directional growth was pointed out by P. Peleé and A. Pumir, J. Cryst. Growth 73, 337 (1985).ADSCrossRefGoogle Scholar
  18. 12.
    E.A. Brener, M.B. Geilikman and D.E. Temkin, Sov. Phys. JETP 67, 1002 (1988).Google Scholar
  19. 12a.
    The problem of growth in a channel was considered earlier by D. Kessler, J. Koplik and H. Levine, Phys. Rev. A 34, 4980 (1986). Brener et al. were the first to find the second upper branch (Fig. 2) which is relevant for directional growth.ADSCrossRefGoogle Scholar
  20. 13.
    P. Pelcé, Europhys. Lett. 7, 453 (1988).ADSCrossRefGoogle Scholar
  21. 14.
    P. Kurowski, Thèse d’Université, Paris 7, 1990; P. Kurowski, C. Guthmann and S. de Cheveigné (to be published).Google Scholar
  22. 15.
    A. Classen, C. Misbah, H. Miiller-Krumbhaar and Y. Saito, Directional solidi-fication with interface dissipation, to appear in Phys. Rev. A 43, 6920 (1991).Google Scholar
  23. 15a.
    Some aspects of the transition to kinetically controlled dendrites were discussed by E. Ben-Jacob, P. Garik and D. Grier, Superlattices and Microstructures 3, 599 (1987).ADSCrossRefGoogle Scholar
  24. 16.
    E.A. Brener and V.I. Mel’nikov, Adv. in Physics, 40, 53 (1991).MathSciNetADSCrossRefGoogle Scholar
  25. 17.
    E. Raz, S.G. Lipson, and E. Polturak, Phys. Rev. A 40, 1088 (1989).ADSCrossRefGoogle Scholar
  26. 18.
    See for example P. Manneville, Dissipative structures and weak turbulence, (Academic Press, New York 1990).MATHGoogle Scholar
  27. 19..
    J.M. Flesselles, A.J. Simon and A.J. Libchaber, Dynamics of one-dimensional interfaces: An experimentalist’s view, preprint 1990, to appear in Advances in Physics.Google Scholar
  28. 20.
    K.A. Jackson and J.D. Hunt, Trans. Mettal. Soc. AIME 236, 1129 (1966).Google Scholar
  29. 21.
    M. Rabaud, S. Michalland and Y. Couder, Phys. Rev. Lett. 64, 184 (1990).ADSCrossRefGoogle Scholar
  30. 22.
    P. Coullet, R.E. Goldstein and G.H. Gunaratne, Phys. Rev. Lett. 63, 1954 (1989).ADSCrossRefGoogle Scholar
  31. 23.
    K. Kassner and C. Misbah, Phys. Rev. Lett. 65, 1458 (1990); erratum Phys. Rev. Lett. 66, (1991).ADSCrossRefGoogle Scholar
  32. 23a.
    For the counting argument and the parity-breaking problem in directional growth of liquid crystals, see also H. Levine and W. Rappel, Phys. Rev. A 42, 7475 (1990).ADSCrossRefGoogle Scholar
  33. 24.
    For a review see G. Lesoult, Ann. Chim. Fr. 5, 154 (1980).Google Scholar
  34. 25.
    K. Kassner and C. Misbah, Phys. Rev. Lett. 66, 445 (1991).MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • K. Kassner
    • 1
  • C. Misbah
    • 2
  • H. Müller-Krumbhaar
    • 4
  • Y. Saito
    • 3
  • D. E. Temkin
    • 4
  1. 1.Inst. f. FestkörperforschungForschungszentrum JülichGermany
  2. 2.GPS, associé au CNRSParisFrance
  3. 3.Physics DepartmentKeio UniversityYokohamaJapan
  4. 4.I.P. Bardin Institute for Ferrous MetalsMoscowUSSR

Personalised recommendations